where \(S_{AL_{p,t}}^{(j)}(\tau _p)\)  denotes the AL log-score of [1]}, corresponding to model \(j\)  and asset \(p\) :
\(S_{AL_{p,t}}^{(j)}(\tau _p)= -\log \left(\frac{\tau _p-1}{ES^{(j)}_{p,t}}\right) - \frac{\left(y_{p,t} - {\cal Q}_{p,t}^{(j)}\right)\left(\tau _p - \mathbf {1}_{(y_{p,t} < {\cal Q}_{p,t}^{(j)})}\right)}{\tau _p ES_{p,t}^{(j)}}.\) 
